JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q26

MathematicsInteger+4 / -1Question 26 of 90

If $n(2n+1)\displaystyle\int_0^1\left(1-x^n\right)^{2n}dx=1177\int_0^1\left(1-x^n\right)^{2n+1}dx$ , then $n\in\mathbf N$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 24

Reduction. $I_{m}=\dfrac{mn}{mn+1}I_{m-1}$ for $I_m=\int_0^1(1-x^n)^mdx$ , so $I_{2n+1}=\dfrac{n(2n+1)}{n(2n+1)+1}I_{2n}$ .

Equation $n(2n+1)+1=1177$ : $n=24$ .

Answer: 24

JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 26